71 Problem 3 1 The two unit tothe line y x 5 are and and and

7.1: Problem 3 1. The two unit tothe line y =x+ 5 are and and and score is 096.

Solution

first of all I\'d find a vector parallel to the line, and in order to do that you can either choose any two points P and Q on the line and consider the vector P - Q or write the line in parametric form
x = t
y = t + 5,
where the coefficients of t are the components of a parallel vector.
So you see that the line is parallel to the vector (1, 1). This vector has length
l = sqrt(1^2 + 1^2) = sqrt(2),
so a unit vector parallel to (1, 1) would be
v = 1/sqrt(2) (1, 1) = (1/sqrt(2), 1/sqrt(2)) = (sqrt(2)/2, sqrt(2)/2).
Once you have find one the other is just its opposite, that is
w = -v = -(sqrt(2)/2, sqrt(2)/2) = (-sqrt(2)/2, -sqrt(2)/2).